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The History of the History of Mathematics

Case Studies for the Seventeenth, Eighteenth and Nineteenth Centuries

Benjamin Wardhaugh

The writing of mathematical histories has a long history, one which has seldom received scholarly attention. Mathematical history, and mathematical biography, raise distinctive issues of method and approach to which different periods have responded in different ways. At a time of increasing interest in the history of mathematics, this book attempts to show something of the trajectory that history has taken in the past. It presents seven case studies illustrating the different ways that mathematical histories have been written since the seventeenth century, ranging from the ‘historia’ of John Wallis to the recent re-presentation of Thomas Harriot’s manuscripts online. It considers both the ways that individual reputations and biographies have been shaped differently in different circumstances, and the ways that the discipline of mathematics has itself been variously presented through the writing of its history.


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‘It must have commenced with mankind’: some ancient histories of arithmetic in eighteenth-century Britain 31


Benjamin Wardhaugh All Souls College, Oxford ‘It must have commenced with mankind’: some ancient histories of arithmetic in eighteenth-century Britain Very little is known of the origin and invention of arithmetic. In fact it must have commenced with mankind, or as soon as they began to hold any sort of commerce together; and must have undergone continual improvements, as occasion was given by the extension of commerce, and by the discovery and cultivation of other sciences. It is therefore very probable that the art has been greatly indebted to the Phœnicians or Tyrians; and indeed Proclus, in his commentary on the first book of Euclid, says, that the Phœnicians, by reason of their traf fic and commerce, were accounted the first inventors of Arithmetic.1 This description of the early history of arithmetic, from Charles Hutton’s 1795–6 Mathematical and Philosophical Dictionary, presents a series of distinctive or surprising features and small puzzles, whose elucidation can help to understand how mathematical history was thought about in eight- eenth-century Britain. Hutton presents arithmetic as profoundly linked to practical considerations, as against the implied alternative of mathematics as fundamentally an abstract study; he yokes it to ‘commerce’ in particular, rather than to any of the other uses to which arithmetic was in fact put in the early modern world. His willingness to speculate about the origin of the subject in primitive societies and his confidence in writing, albeit very brief ly, about its early history, sit uneasily with the paucity of...

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